Longitudinal waves are waves in which the displacement of the medium is in the same (or opposite) direction of the wave propagation. Mechanical longitudinal waves are also called ''compressional'' or compression waves, because they produce compression
when traveling through a medium, and pressure waves, because they produce increases and decreases in pressure. Sound travels through longitudinal waves. Sound travels through transversal waves in 90 degrees.
The other main type of wave is the transverse wave
, in which the displacements of the medium are at right angles to the direction of propagation. Transverse waves, for instance, describe ''some'' bulk sound waves in solid materials (but not in fluids); these are also called "shear waves" to differentiate them from the (longitudinal) pressure waves that these materials also support.
Longitudinal waves include sound waves (vibration
s in pressure, a particle of displacement, and particle velocity propagated in an elastic
medium) and seismic P-wave
s (created by earthquakes and explosions).
In longitudinal waves, the displacement of the medium is parallel to the propagation of the wave. A wave along the length of a stretched Slinky
toy, where the distance between coils increases and decreases, is a good visualization and contrasts with the standing wave
along an oscillating guitar string which is transverse.
"Longitudinal waves" and "transverse waves" have been abbreviated by some authors as "L-waves" and "T-waves", respectively, for their own convenience. While these two abbreviations have specific meanings in seismology
(L-wave for Love wave
or long wave) and electrocardiography
(see T wave
), some authors chose to use "l-waves" (lowercase 'L') and "t-waves" instead, although they are not commonly found in physics writings except for some popular science books.
In the case of longitudinal harmonic sound waves, the frequency
can be described by the formula
* ''y'' is the displacement of the point on the traveling sound wave;305px|Representation of the propagation of an omnidirectional pulse wave on a 2d grid (empirical shape)
* ''x'' is the distance the point has traveled from the wave's source;
* ''t'' is the time elapsed;
is the amplitude
of the oscillations,
* ''c'' is the speed of the wave; and
* ''ω'' is the angular frequency
of the wave.
The quantity ''x''/''c'' is the time that the wave takes to travel the distance ''x''.
The ordinary frequency (''f'') of the wave is given by
The wavelength can be calculated as the relation between a wave's speed and ordinary frequency.
For sound waves, the amplitude of the wave is the difference between the pressure of the undisturbed air and the maximum pressure caused by the wave.
Sound's propagation speed
depends on the type, temperature, and composition of the medium through which it propagates.
The equations for sound in a fluid given above also apply to acoustic waves in an elastic solid. Although solids also support transverse waves (known as S-waves
), longitudinal sound waves in the solid exist with a velocity
and wave impedance
dependent on the material's density
and its rigidity
, the latter of which is described (as with sound in a gas) by the material's bulk modulus
lead to the prediction of electromagnetic wave
s in a vacuum, which is strictly transverse wave
s, that is, the electric and magnetic fields of which the wave consists are perpendicular to the direction of the wave's propagation.
[David J. Griffiths, Introduction to Electrodynamics, ]
However plasma wave
s are longitudinal since these are not electromagnetic waves but density waves of charged particles, but which can couple to the electromagnetic field.
's attempts to generalize Maxwell's equations
, Heaviside concluded that electromagnetic waves were not to be found as longitudinal waves in "''free space
''" or homogeneous media. Maxwell's equations, as we now understand them, retain that conclusion: in free-space or other uniform isotropic dielectrics, electro-magnetic waves are strictly transverse. However electromagnetic waves can display a longitudinal component in the electric and/or magnetic fields when traversing birefringent
materials, or inhomogeneous materials especially at interfaces (surface waves for instance) such as Zenneck wave
In the development of modern physics, Alexandru Proca
(1897-1955) was known for developing relativistic quantum field equations bearing his name (Proca's equations) which apply to the massive vector spin-1 mesons. In recent decades some other theorists, such as Jean-Pierre Vigier
and Bo Lehnert of the Swedish Royal Society, have used the Proca equation in an attempt to demonstrate photon mass
as a longitudinal electromagnetic component of Maxwell's equations, suggesting that longitudinal electromagnetic waves could exist in a Dirac polarized vacuum. However photon rest mass
is strongly doubted by almost all physicists and is incompatible with the Standard Model
* Transverse wave
* Acoustic wave
* Plasma waves
* Varadan, V. K., and Vasundara V. Varadan, "''Elastic wave scattering and propagation''". ''Attenuation due to scattering of ultrasonic compressional waves in granular media'' - A.J. Devaney, H. Levine, and T. Plona. Ann Arbor, Mich., Ann Arbor Science, 1982.
* Schaaf, John van der, Jaap C. Schouten, and Cor M. van den Bleek, "''Experimental Observation of Pressure Waves in Gas-Solids Fluidized Beds''". American Institute of Chemical Engineers. New York, N.Y., 1997.
* Russell, Dan, "Longitudinal and Transverse Wave Motion
'". Acoustics Animations, Pennsylvania State University, Graduate Program in Acoustics.
* Longitudinal Waves, with animations "
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